Riemannian Loss for Image Restoration

Abstract

Deep neural networks are widely used for image restoration, however the loss criteration is usually set as l2.ll2 penalizes larger errors, which is unstable for outliers. To avoid the disadvantages, l1 is utilized as a more robust and well behaved loss. This paper proposes a novel loss function for restoration networks, which measures geodesic distance in Riemannian manifold and exploits the outstanding properties of l1. Different from l1 and l2 loss which reflects pixel distance, our loss in Riemannian reflects the structure distance of image. The proposed loss not only preserves the robutness of l1 loss, but also reflects the image contrasts. Experimental results on image super resolution and compressed sensing show that our proposed loss function achieves more accurate reconstructions, according to both the objective and perceptual qualities.